Abstract-This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) algorithm for massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with M antennas serves K Gaussian sources simultaneously. Both K and M are very large numbers, and we consider the cases that K < M . The GMPID is a low-complexity message passing algorithm based on a fully connected loopy graph, which is well understood to be not convergent in some cases. As it is hard to analyse the GMPID directly, the large-scale property of the massive MU-MIMO is used to simplify the analysis. Firstly, we prove that the variances of the GMPID definitely converge to the mean square error of Minimum Mean Square Error (MMSE) detection. Secondly, we propose two sufficient conditions that the means of the GMPID converge to those of the MMSE detection. However, the means of GMPID may not converge when K/M ≥ ( √ 2 − 1) 2 . Therefore, a new convergent GMPID called SA-GMPID (scale-and-add GMPID) , which converges to the MMSE detection in mean and variance for any K < M and has a faster convergence speed than the GMPID, but has no higher complexity than the GMPID, is proposed. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results.

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Currently, methods for protein detection are not as sensitive and specific as methods for detection of specific nucleic acid sequences. Here, we present an analogous technique for detection of proteins using aptamers as ligands for target binding. We have named this method the aptamer-based exonuclease protection assay. We applied a special oligonucleotide probe containing a thrombin aptamer, which has the capacity to recognize thrombin with high affinity and specificity. The aptamer probe is a 22-base-long single-strand oligonucleotide with the thrombin aptamer sequence at the 3'-terminus and 7 additional nucleotides at the 5'-terminus, which is able to bind thrombin with high affinity and specificity. In the exonuclease protection assay, thrombin binds the aptamer and thereby protects it from degradation by exonuclease I, whereas any unbound aptamer probe is degraded by exonuclease I. Subsequently, the aptamer probes that were protected from exonuclease I by thrombin act as linkers to join two free connectors, which contain sequences matching the probe. The joined products, which reflect the identity and amount of the target protein, are amplified by PCR. The exonuclease protection assay is extremely sensitive, since it is based on PCR amplification. This method can detect as few as several hundred molecules of target protein without using washes or separations. In addition, this new method for protein detection is simple and inherits all the advantages of aptamers. The mechanism, moreover, may be generalized and used for other forms of protein analysis.

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) method over a pairwise graph for a massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with M antennas serves K Gaussian sources simultaneously. Both K and M are large numbers and we consider the cases that K < M in this paper. The GMPID is a message passing algorithm based on a fully connected loopy graph, which is well known that it is not convergent in some cases. In this paper, we first analyse the convergence of GMPID. Two sufficient conditions that the GMPID converges to the Minimum Mean Square Error (MMSE) detection are proposed. However, the GMPID may still not converge when K/M > ( √ 2 − 1) 2 . Therefore, a new convergent GMPID with equally low complexity called SA-GMPID is proposed, which converges to the MMSE detection for any K < M with a faster convergence speed. Finally, numerical results are provided to verify the validity and accuracy of the proposed theoretical results.

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